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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Online
ISSN
1569-3945
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Volume 23, Issue 1

Issues

Inverse problems for linear degenerate parabolic equations by “time-like” Carleman estimate

Atsushi Kawamoto
Published Online: 2014-07-02 | DOI: https://doi.org/10.1515/jiip-2013-0027

Abstract

In this paper, we study inverse problems for multi-dimensional linear degenerate parabolic equations and strongly coupled systems. In particular we discuss the Lipschitz type stability results for the inverse source problems which determine a source term by boundary data on an appropriate sub-boundary and the data on any fixed time. Our arguments are based on the Carleman estimate. Here we prove and use the Carleman estimate with the x-independent weight function for linear degenerate parabolic equations and systems.

Keywords: Carleman estimate; inverse source problem; conditional stability; uniqueness; linear degenerate parabolic equation

MSC: 35B45; 35R30; 35K65

About the article

Received: 2013-04-10

Revised: 2014-03-26

Accepted: 2014-06-14

Published Online: 2014-07-02

Published in Print: 2015-02-01


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 23, Issue 1, Pages 1–21, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2013-0027.

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Journal of Inverse and Ill-posed Problems, 2017, Volume 0, Number 0
[2]
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Computational Mathematics and Mathematical Physics, 2017, Volume 57, Number 5, Page 833

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